South Korea's President Park Geun-hye faces calls to quit, as a national security scandal inflames political uncertainty in Asia's fourth-largest economy.

In a rare televised public apology this week, the 64-year-old leader admitted she received help on state affairs from an old friend and informal advisor called Choi Soon-sil. Choi, who holds no post in government, provided advice on speeches and public relations issues during the 2012 presidential election campaign and continued to assist for a period after the 2013 inauguration, Park said.

Several reports in South Korean media suggested that Choi also had access to classified material related to national security and economic policies. And there has been widespread speculation that Choi may have interfered in key government affairs, and exploited her connections to Park to establish two nonprofit foundations using funds from corporate donations. On Thursday, prosecutors established a task-force to probe the unfolding development.

The so-called "Choi-gate" scandal has been compared to the uproar over U.S. presidential candidate Hillary Clinton's decision to use a private server for her government emails while she was secretary of state.

Choi, 60, is the daughter of Park's late mentor Choi Tae-min. In mid-1970s, the latter introduced his daughter to Park, who was then acting as first lady following her mother's assassination, and the two women have been friends ever since, according to local media.

The media backlash over Park's apparent indiscretions has been fierce.

"In Park's mind, there has never been a distinction between public and private," said a scathing editorial in Wednesday's edition of independent newspaper The Hankyoreh. "She had no awareness of the importance of protecting important state secrets or of the danger of such secrets being leaked....The current commander in chief of the Republic of Korea lacks the basic attitude required of public servants."

JUNG YEON-JE | AFP | Getty Images

Protesters hang a caricature showing President Park Geun-Hye (L) and her confidante Choi Soon-Sil (C) during a rally in Seoul on October 27, 2016.

Meanwhile, the economic implications could be significant.

"We believe the backlash in political circles could delay the National Assembly's passage of the 2017 budget as well as other economic reform policies in the pipeline, including corporate restructuring," Citi economist Jaechul Chang said in a Thursday note. "More broadly, heightened political tensions will erode broader economic sentiment and slow Korea's recovery."

"Choi-gate" is also likely to hurt Park's constitutional reforms. On Monday, she proposed a multiple-term presidency for future heads of state, instead of the current single five-year term rule. Park's first term ends in February 2018.

"The president's weakening clout and lame-duck status are likely to slow her efforts to pass a constitutional amendment that would introduce a semi-presidential system," Chang said.

Park's approval rating stood at 17.5 percent on Wednesday, according to a nationwide survey by Realmeter, with 43 percent of survey respondents demanding her resignation. Her political opponents have already called for parliamentary investigations and her withdrawal from the ruling party.

Should Park resign, it would cap a messy period for Korean politics. Prime Minister Lee Wan-koo tendered his resignation in 2015 just two months into the post, amid allegations of bribery. More recently, influential politician Ahn Cheol Soo stepped down in June as co-chair of a new opposition group, called the People's Party, over claims of graft.

Polls indicate outgoing U.N. Secretary-General Ban Ki-moon, a South Korean native, is the favorite to replace Park. The 72-year-old told Reuters last week that he would return to his home country in January to consider "what kind of role he can play for the future of Korea."